The neural network models with delays for solving absolute value equations
This work addresses a specific mathematical problem in computational mathematics, offering an incremental improvement over existing neural network methods for solving AVEs.
The authors tackled solving absolute value equations (AVEs) by proposing inverse-free neural network models with mixed delays, proving exponential convergence using Lyapunov-Krasovskii theory and LMI methods, and demonstrating effectiveness through numerical simulations for AVEs with ||A^{-1}|| > 1.
An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) $Ax -|x| - b =0$, which includes an inverse-free neural network model with discrete delay as a special case. By using the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the developed neural network models are proved to be exponentially convergent to the solution of the AVE. Compared with the existing neural network models for solving the AVE, the proposed models feature the ability of solving a class of AVE with $\|A^{-1}\|>1$. Numerical simulations are given to show the effectiveness of the two delayed neural network models.